Fundamental Theorem of Functions

by Open Science Repository Mathematics
(August 2014)

Abstract

From the fundamental theorem of homomorphisms, it is well known that any homomorphism of groups can be decomposed as a composition of a monomorphism and an epimorphism. This result can also be extended to general functions defined on abstract sets; that is, any function can be expressed as a composition of an injection and a surjection.

The main theorem in this research called ‘Fundamental theorem of functions’ provides the uniqueness of such a decomposition of functions as a composition of an injection and a surjection. The uniqueness in this theorem is proved upto the level of associates by introducing the notion of an associate of functions.

Keywords: injections, surjections, composition of functions, associate of a function, uniqueness up to associate.

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Fundamental Theorem of Functions